Method, apparatus and computer program product for providing pattern detection with unknown noise levels

ABSTRACT

An apparatus for providing pattern detection may include a processor. The processor may be configured to iteratively test different models and corresponding scales for each of the models. The models may be employed for modeling parameters corresponding to a visually detected data. The processor may be further configured to evaluate each of the models over a plurality of iterations based on a function evaluation of each of the models, select one of the models based on the function evaluation of the selected one of the models, and utilize the selected one of the models for fitting the data.

TECHNOLOGICAL FIELD

Embodiments of the present invention relate generally to patterndetection and, more particularly, relate to an apparatus, method andcomputer program product for enabling pattern detection with unknownnoise levels.

BACKGROUND

Electronic computing devices are becoming increasingly ubiquitous in themodern world. Whether utilized for business, entertainment,communication, security or numerous other purposes, the capabilities ofsuch devices continue to expand. Along with the improvements made interms of processing power, rendering technology, memory, powerconsumption and other aspects, various applications have also beendeveloped to utilize the expanded capabilities of computing devices.However, the expansion of capabilities with respect to such devices hasalso introduced new sets of challenges as further improvements aresought and new applications are developed.

One area in which the use of electronic computing devices has presentednew challenges relates to computer vision. Computer vision utilizesmachines to see. As such, for example, computer vision often employscameras and other elements to build systems that can obtain informationfrom image data such as a video sequence, views from multiple cameras ormultidimensional data from scanning devices. Computer vision may beuseful for many tasks such as: controlling processes or devicemovements; detecting and/or recognizing events, objects, patterns orpeople; organizing information; and/or the like. Accordingly, computervision may be considered to be an artificial vision system, which may beimplemented in combinations of various devices and applications.

One common situation encountered in computer vision relates to thefitting of noisy data with parametric models in the presence of highratio noise. Existing technologies such as Hough transformations, RANSAC(random sample consensus), and improvements of these technologies areoften utilized in such situations. However, Hough transformation andRANSAC based approaches are typically employed best in environments withknown noise levels. In particular, both Hough transformation and RANSACbased approaches require the entry of a threshold or otheruser-specified control parameters, which may be difficult for users toestimate when noise levels are unknown. Accordingly, improvements in thearea of pattern detection in environments with unknown noise levels maybe desirable.

BRIEF SUMMARY OF EXEMPLARY EMBODIMENTS

A method, apparatus and computer program product are therefore providedthat may enable devices to provide improved pattern detection inenvironments with unknown noise levels. In particular, some embodimentsof the present invention may provide for model fitting without requiringuser specified parameters. As such, for example, embodiments of thepresent invention may be enabled to simultaneously estimate parameters(e.g., a threshold), that would normally be provided by a user, andestimate a model, without any user-specified parameters. In this regard,embodiments of the present invention may enable an estimation of thescale of inlier noise to improve the accuracy of fitting results in thecourse of sampling and may also provide for use of ensemble inlier setsfor guided sampling. Moreover, embodiments of the present invention maybe more efficient than existing approaches.

In one exemplary embodiment, a method of providing pattern detection isprovided. The method may include iteratively testing different modelsand corresponding scales for each of the models. The models may beemployed for modeling parameters corresponding to a visually detecteddata. The method may further include evaluating each of the models overa plurality of iterations based on a function evaluation of each of themodels, selecting one of the models based on the function evaluation ofthe selected one of the models, and utilizing the selected one of themodels for fitting the data.

In another exemplary embodiment, a computer program product forproviding pattern detection is provided. The computer program productmay include at least one computer-readable storage medium havingcomputer-executable program code portions stored therein. Thecomputer-executable program code portions may include a first programcode instructions, second program code instructions, third program codeinstructions and fourth program code instructions. The first programcode instructions may be for iteratively testing different models andcorresponding scales for each of the models. The models may be employedfor modeling parameters corresponding to a visually detected data. Thesecond program code instructions may be for evaluating each of themodels over a plurality of iterations based on a function evaluation ofeach of the models. The third program code instructions may be forselecting one of the models based on the function evaluation of theselected one of the models. The fourth program code instructions may befor utilizing the selected one of the models for fitting the data.

In another exemplary embodiment, an apparatus for providing patterndetection is provided. The apparatus may include a processor that may beconfigured to iteratively test different models and corresponding scalesfor each of the models. The models may be employed for modelingparameters corresponding to a visually detected data. The processor maybe further configured to evaluate each of the models over a plurality ofiterations based on a function evaluation of each of the models, selectone of the models based on the function evaluation of the selected oneof the models, and utilize the selected one of the models for fittingthe data.

In another exemplary embodiment, an apparatus for providing patternrecognition is provided. The apparatus may include means for iterativelytesting different models and corresponding scales for each of themodels. The models may be employed for modeling parameters correspondingto a visually detected data. The apparatus may further include means forevaluating each of the models over a plurality of iterations based on afunction evaluation of each of the models, means for selecting one ofthe models based on the function evaluation of the selected one of themodels, and means for utilizing the selected one of the models forfitting the data.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING(S)

Having thus described the invention in general terms, reference will nowbe made to the accompanying drawings, which are not necessarily drawn toscale, and wherein:

FIG. 1 is a schematic block diagram of a computer vision systemaccording to an exemplary embodiment of the present invention;

FIG. 2 is a schematic block diagram of an apparatus for providingpattern recognition according to an exemplary embodiment of the presentinvention; and

FIG. 3 is an illustration of different algorithms employed for fittingdata for providing pattern recognition according to an exemplaryembodiment of the present invention;

FIG. 4 is an illustration of different algorithms employed for fittingalternative data for providing pattern recognition according to anexemplary embodiment of the present invention;

FIG. 5A-5D show an example of fundamental matrix estimation inaccordance with an exemplary embodiment of the present invention whereinFIGS. 5A and 5B show 104 true inliers (stars) and 150 outliers (dots)uniformly distributed over images and wherein FIGS. 5C and 5D show aRANSAC-EIS-Metropolis fitting result with 100 inliers, in which 94 aretrue inliers and 6 mismatch; and

FIG. 6 is a flowchart according to an alternative exemplary method ofproviding pattern recognition according to an exemplary embodiment ofthe present invention.

DETAILED DESCRIPTION

Some embodiments of the present invention will now be described morefully hereinafter with reference to the accompanying drawings, in whichsome, but not all embodiments of the invention are shown. Indeed,various embodiments of the invention may be embodied in many differentforms and should not be construed as limited to the embodiments setforth herein; rather, these embodiments are provided so that thisdisclosure will satisfy applicable legal requirements. Like referencenumerals refer to like elements throughout. As used herein, the terms“data,” “content,” “information” and similar terms may be usedinterchangeably to refer to data capable of being transmitted, receivedand/or stored in accordance with embodiments of the present invention.Moreover, the term “exemplary”, as used herein, is not provided toconvey any qualitative assessment, but instead merely to convey anillustration of an example. Thus, use of any such terms should not betaken to limit the spirit and scope of embodiments of the presentinvention.

Many computer vision problems essentially boil down to a problem offitting noisy data with parametric models. This problem is oftencomplicated by the presence of outliers (e.g., data points that do notsatisfy a given model relation). The solution may be formulated as a MAP(maximum a posterior) estimation of a model parameter θ, given inputdata D and a user-specified threshold ε differentiating outliers frominliers as indicated in equation 1 below.

$\begin{matrix}{\left\lbrack \hat{\theta} \right\rbrack = {\arg\;{\max\limits_{\theta}{{p\left( {\left. \theta \middle| D \right.,ɛ} \right)}.}}}} & (1)\end{matrix}$

For specific problems, it may be possible to evaluate a likelihoodfunction L(θ|D, ε) (or simply L(θ)) at certain discrete values of θ.From Bayesian theorem, the posterior distribution may be partially knownup to a normalization constant:p(θ|D,ε)∝L(θ|D,ε)p(θ).  (2)If the priori distribution p(θ) is assumed uniform, it may be possibleto seek maximum likelihood (ML) estimation using equation 3 below.

$\begin{matrix}{\left\lbrack \hat{\theta} \right\rbrack = {\arg\;{\max\limits_{\theta}{{L\left( {\left. \theta \middle| D \right.,ɛ} \right)}.}}}} & (3)\end{matrix}$

For many computer vision problems, high outlier ratio data may renderstandard least squares fitting relatively useless. The likelihoodfunction may account for the statistical nature of inliers and outliermodels. Often, a set of indicator variables γ=[γ₁ . . . γ_(N)] may beassigned such that γ_(i)=1 if the ith corresponding data point is aninlier and γ_(i)=0 otherwise. In this regard, for example, a mixturemodel of Gaussian and uniform distributions may be used in the contextof multiview geometry estimation

$\begin{matrix}{{L\left( {\left. \theta \middle| D \right.,ɛ} \right)} = {\sum\limits_{i = 1}^{N}\left( {\log\left( {{\gamma_{i}\frac{1}{\sqrt{2{\pi\sigma}^{2}}}{\exp\left( {- \frac{e_{i}^{2}}{2\sigma^{2}}} \right)}} + {\left( {1 - \gamma_{i}} \right)\frac{1}{\upsilon}}} \right)} \right)}} & (4)\end{matrix}$where e_(i) stands for the ith data point error, and v is the volume ofthe uniform distribution for outliers. While γ depends on (θ, D, ε), itmay not be possible to express a specific formula for γ(θ, D, ε) andoptimize equation (3) directly. Instead a RANSAC algorithm may be usedto make an estimate of inlier sets.

However, RANSAC has a sensitivity to a user specified threshold and thescale of inlier noise. Accordingly, embodiments of the present inventionmay iteratively make estimates of scale for various proposed models. Asan example, embodiments of the present invention may provides amechanism by which, according to equation (5) below,

$\begin{matrix}{\left\lbrack {\hat{\theta},\hat{ɛ}} \right\rbrack = {\arg\;{\max\limits_{\theta,ɛ}{{L\left( {\theta,\left. ɛ \middle| D \right.} \right)}.}}}} & (5)\end{matrix}$various models and a corresponding scale for each may be iterativelytested over a plurality of iterations. In equation (5), L may beconsidered to correspond to an objective evaluation of a given model,such that the higher the value of L, the better the model. Thus, thefunction evaluation may provide an indication of how well ε and θ fitthe data D.

Some embodiments of the present invention may enable the simultaneousdetermination of both scale estimation and a best model including modelparameters for fitting data in a noisy environment. The scale estimationmay provide a scale of inlier data points among a plurality of noisydata points. As such, outlier data points may be disregarded and asmaller set of points may be considered for improving samplingefficiency for a fitting problem. Accordingly, embodiments of thepresent invention may provide a robust method for estimating a scale ofinlier noise in the course of random sampling and may provide for anensemble inlier set for guided sampling. The scales may be derived fromstatistics of repeated inlier data points accumulated from variousdifferent proposed models. The use of accumulated inlier data points,which may be defined as the ensemble inlier set, may provide arelatively simple and efficient computational tool to classify inliersand outliers within a data set. The probabilistic inlier/outlierclassification may then be used to attenuate effects of extreme outliersby providing a resultant scale estimator (e.g., weighted median absolutedeviation (WMAD)), which may improve fitting result accuracy. The guidedsampling approach does not require any auxiliary information, such asmatch scores, to be provided, and therefore lends itself well to beingused in different fitting problems.

As discussed above, embodiments of the present invention may bepracticed in the context of a computer vision system. As such, anexemplary embodiment will now be described in reference to FIG. 1, whichillustrates a basic block diagram of a system for employing a computervision system. However, it should be appreciated that embodiments of thepresent invention could be practiced in numerous other pattern detectionenvironments and are not limited to application in connection withcomputer vision systems. Moreover, even in connection with computervision systems, it should be recognized that FIG. 1 is merely one basicexample of such a system and should not be seen as limiting in any way.

Referring now to FIG. 1, a computer vision system 10 may include animage capturing module 20 and a computing device 30. The image capturingmodule 20 may include one or more cameras or other image capturingsensors configured to capture image data. The image data may be in theform of, for example, a video sequence or one or more images from one ormore respective cameras or sensors. The computing device 30 may be acomputer (e.g., a personal computer, laptop, server, or the like), amobile telephone, global positioning system (GPS) device, a personaldigital assistant (PDA), pager, mobile television, gaming device,camera, audio/video player, radio, or any combination of theaforementioned, and other types of electronic devices that may include aprocessor and/or memory for executing various hardware and/or softwareprocesses. The computing device 30 may be configured to employprocessing in accordance with embodiments of the present invention asdescribed in greater detail below in connection with the description ofFIG. 2.

Communication between the image capturing module 20 and the computingdevice 30 may be real-time or near real-time via either wired orwireless transmission mechanisms. In some cases, the communicationbetween the image capturing module 20 and the computing device 30 may beintermittent or delayed. Furthermore, in some situations, the imagecapturing module 20 may store image data, which may then be communicatedto the computing device 30 at a later time (directly or via anintermediate device). However, in some embodiments, the image capturingmodule 20 and the computing device 30 may be portions of a single device(e.g., a mobile terminal or phone with a built in camera). In somecases, the computing device 30 may be in communication with otherdevices via a network 40, although no network connection is required.

Referring now to FIG. 2, a schematic block diagram of an apparatus 50for providing pattern recognition according to an exemplary embodimentof the present invention is provided. The apparatus 50 may include orotherwise be in communication with a processor 70, a user interface 72,a communication interface 74 and a memory device 76. However, theapparatus 50 may further include additional elements as described ingreater detail below. In this regard, it should be understood that theexemplary embodiment of FIG. 2 is provided merely for exemplary purposesand thus other configurations for the apparatus 50 are also possible.Moreover, certain elements shown in FIG. 2 may be split between multipledevices (e.g., operating in a client/server relationship) or may all beembodied at the same device.

The memory device 76 may include, for example, volatile and/ornon-volatile memory. Volatile memory 40 may include Random Access Memory(RAM) including dynamic and/or static RAM, on-chip or off-chip cachememory, and/or the like. Non-volatile memory, which may be embeddedand/or removable, may include, for example, read-only memory, flashmemory, magnetic storage devices (e.g., hard disks, floppy disk drives,magnetic tape, etc.), optical disc drives and/or media, non-volatilerandom access memory (NVRAM), and/or the like. Like volatile memory,non-volatile memory may include a cache area for temporary storage ofdata. The memory device 76 may store any of a number of pieces ofinformation, and data, used by the apparatus 50 to implement thefunctions of the apparatus 50. The memory device 76 may be configured tostore information, data, applications, instructions or the like forenabling the apparatus to carry out various functions in accordance withexemplary embodiments of the present invention. For example, the memorydevice 76 may be configured to buffer input data for processing by theprocessor 70. Additionally or alternatively, the memory device 76 may beconfigured to store instructions for execution by the processor 70. Asyet another alternative, the memory device 76 may be one of a pluralityof databases that store information and/or media content.

The processor 70 may be embodied in a number of different ways. Forexample, the processor 70 may be embodied as various processing meanssuch as a processing element, a coprocessor, a controller or variousother processing devices including integrated circuits such as, forexample, an ASIC (application specific integrated circuit), an FPGA(field programmable gate array), a hardware accelerator, and/or thelike. In an exemplary embodiment, the processor 70 may be configured toexecute instructions stored in the memory device 76 or otherwiseaccessible to the processor 70. Additionally or alternatively, theprocessor 70 may be configured to direct or control the operation ofother modules or functional elements to effect operations in accordancewith embodiments of the present invention.

The communication interface 74 may be embodied as any device or meansembodied in either hardware, software, or a combination of hardware andsoftware that is configured to receive and/or transmit data from/to anetwork and/or any other device or module in communication with theapparatus 50. In this regard, the communication interface 74 mayinclude, for example, an antenna and supporting hardware and/or softwarefor enabling communications with a wireless communication network. Infixed environments, the communication interface 74 may alternatively oralso support wired communication. As such, the communication interface74 may include a communication modem and/or other hardware/software forsupporting communication via cable, digital subscriber line (DSL),universal serial bus (USB) or other mechanisms.

The user interface 72 may be in communication with the processor 70 toreceive an indication of a user input at the user interface 72 and/or toprovide an audible, visual, mechanical or other output to the user. Assuch, the user interface 72 may include, for example, a keyboard, amouse, a joystick, a touch screen, a display, a microphone, a speaker,or other input/output mechanisms. In an exemplary embodiment in whichthe apparatus is embodied as a server, the user interface 72 may belimited, or eliminated.

In some embodiments, the apparatus 50 may include or be in communicationwith a media capturing module (e.g., the image capturing module 20),such as a camera, video and/or audio module, in communication with thecontroller 20. The media capturing module may be any means for capturingan image, video and/or audio for storage, display or transmission. Forexample, in an exemplary embodiment in which the media capturing moduleis a camera module 78, the camera module 78 may include a digital cameracapable of forming a digital image file from a captured image or forminga video content file from a sequence of image frames. As such, thecamera module 78 may include all hardware, such as a lens or otheroptical device, and software necessary for creating a digital image filefrom a captured image. Alternatively, the camera module 78 may includeonly the hardware needed to view an image, while a memory device of theapparatus 50 stores instructions for execution by the controller 20 inthe form of software necessary to create a digital image file from acaptured image. In an exemplary embodiment, the camera module 78 mayfurther include a processing element such as a co-processor whichassists the processor 70 in processing image data and an encoder and/ordecoder for compressing and/or decompressing image data. The encoderand/or decoder may encode and/or decode according to a JPEG standardformat or other formats.

In an exemplary embodiment, the processor 70 may be embodied as, includeor otherwise control a scale estimator 80 and a model evaluator 82. Thescale estimator 80 and the model evaluator 82 may each be any means suchas a device or circuitry embodied in hardware, software or a combinationof hardware and software that is configured to perform the correspondingfunctions of the scale estimator 80 and the model evaluator 82 asdescribed below.

The scale estimator 80 may be configured to estimate scale usingstatistics of repeated inlier data points accumulated over a pluralityof proposed models. The model evaluator 82 may be configured to evaluatemodels based on various criteria and enable the selection of aparticular model for fitting operations as described herein. Equation(5) above tends to favor models with a larger number of inlier datapoints. Thus, the function evaluation may provide low weights forrelatively bad models and high weights for relatively good models toresult in a high score for models that give a larger number of inlierpoints. By estimating scale, the scale estimator 80 effectivelyseparates inliers from outliers. For example, as shown in FIG. 3, whichillustrates a two dimensional line segment fitting example with 100inliers and 200 outliers in which the dotted line estimates the linemodel and each solid line identifies the estimated scale, the inlierslay between the solid lines. It should also be noted that the fivedifferent datasets shown in FIG. 3 have each been fit by three differentmethods to show various examples. In this regard, the top fitting ineach dataset is performed using RANSAC with median absolute deviations(MAD), the middle fitting in each dataset is performed using RANSAC withensemble inlier sets (EIS) according to an exemplary embodiment, and thebottom fitting in each dataset is performed using RANSAC with ensembleinlier sets with a Metropolis-Hasting (MH) step. FIG. 4 shows similarresults for ellipse fitting in an example with 100 inliers and 160outliers. As can be seen from FIGS. 3 and 4, the scale (represented bythe distance between the solid lines in FIG. 3 and by the length of thesolid lines in FIG. 4) for fittings using ensemble inlier sets isreduced by each subsequent embodiment employing EIS so that moreoutliers can be excluded from consideration to give a better fit.

In an exemplary embodiment, scale estimation may proceed according tothe description provided below. In this regard, a model may be definedas a parameterized function ƒ(x|θ), where x is a data point and θ is anunknown model parameter. It may be desirable to find models in a set ofN points x_(n)εD, n ε1, 2, . . . N. A point may fit the model whenƒ(x_(n)|θ)=0. For a set of s points, there may exist a unique model θfor which all s points fit perfectly. Such a set may be referred to as aminimal subset and s may be referred to as model dimensionality. As anexample, in line fitting, two points may constitute a minimal subset(e.g., s=2), while in ellipse fitting, s may equal 5. A permissiblemodel of D may be one defined by a minimal subset and all permissiblemodels may form a finite discrete model set Θ.

Given a scale parameter ε, the inlier set for model θ may be given byequation (6) belowI _(ε)(θ)={xεD∥ƒ(x|θ)|≦ε},  (6)in which ƒ(x|θ) is the error of fitting x with θ, and |·| is theabsolute value of the error. The setting of ε may be related to thescale of inlier noise. The inlier set may be referred to as the perfectset I₀(θ) of model θ when ε=0. For a standard RANSAC approach, thelikelihood L is simply taken as the cardinality of inlier sets. Morerobust results may be obtained by taking into account how well inlierpoints fit the estimated model as in equation (4).

If the scale ε is unknown and can be chosen freely, the number ofinliers may take a maximum as {circumflex over (ε)}→∞. One possiblesolution to this problem is to use the likelihood function

$\begin{matrix}{{L\left( {\left. \theta \middle| D \right.,ɛ} \right)} = {\frac{{I_{ɛ}(\theta)}}{ɛ}.}} & (7)\end{matrix}$

Unfortunately, this likelihood function may bring about anotherdegenerate solution {circumflex over (ε)}→θ when any one of minimal setsis selected. As a robust solution to avoid these degenerate cases, itmay be possible to estimate the median absolute deviation (MAD) offitting error

$\begin{matrix}{{{\hat{ɛ}}_{MAD} = {{median}\left( {\left. {{f\left( x_{n} \right.}\theta} \right) - {{median}\left( {f\left( {x_{n}\left. \theta \right)} \right)} \right.}} \right)}};\mspace{11mu}{x_{n} \in D}} & (8)\end{matrix}$and use its inverse as the

$\begin{matrix}{{L\left( \theta \middle| D \right)} = {\frac{1}{{\hat{ɛ}}_{MAD}}.}} & (9)\end{matrix}$

Notice that {circumflex over (ε)}_(MAD) is not a free parameter but amaximum likelihood estimation given D and θ. As such, MAD may be arelatively robust scale estimator with a breakdown point of 0.5 andbounded influence function. MAD may often be used as ancillary scaleestimation for iterative M-estimators. If inlier set distribution isassumed to be Gaussian, the standard deviation may be estimated as:

$\begin{matrix}{\hat{\sigma} = {\frac{{\hat{ɛ}}_{MAD}}{\Phi^{- 1}\left( \frac{3}{4} \right)} = {1.4826*{{\hat{ɛ}}_{MAD}.}}}} & (10)\end{matrix}$

In many computer vision applications, however, MAD may tend toover-estimate when the outlier ratio is high (e.g., >0.5). As amodification to MAD, Weighted Median Absolute Deviation (WMAD) can beused to attenuate effects of extreme outliers:{circumflex over (ε)}_(WMAD) =WM(|ƒ(x _(n)|θ)−WM(x_(n)|θ),ω_(n))|,ω_(n)):x _(n) εD  (11)in which ω_(n), nε[1 . . . N] is a non-negative scalar, proportional tothe probability of each data point being an inlier. Weighted Median (WM)filter is an extension of median filter in that it duplicates eachsample ω_(n) times before taking median of input samples. Like{circumflex over (ε)}_(MAD), the scale estimator in equation (11) maynot be a free parameter, but a quantity uniquely determined by D, θ andweights W=[ω₁ ω₂ . . . ω_(n)]. Accordingly, it may be useful to have amechanism for determining how to assign weights ω_(n) to each data pointfor robust estimation of scales.

It follows from equation (6) that for any given data set D and scale ε,there exists a mapping from a model parameter θ_(i) to its inlier setI_(ε)(θ_(i)). The inlier set may be represented by an indication vectorγ(θ_(i))=[γ₁ . . . γ_(N)] with each component:

$\begin{matrix}{\gamma_{n} = \left\{ {{{\begin{matrix}1 & {{{{if}\mspace{14mu} x_{n}} \in {I_{ɛ}\left( \theta_{i} \right)}},} \\0 & {{otherwise}.}\end{matrix}n} \in 1},2,\ldots\mspace{14mu},{N.}} \right.} & (12)\end{matrix}$

When many new models are proposed, corresponding inlier sets may beaccumulated by summing up γ(θ_(i)). We end up with a weight vector W=[ω₁. . . ω_(N)] associated with all data points:

$\begin{matrix}{W = {\sum\limits_{i = 1}^{T}{{\gamma\left( \theta_{i} \right)}.}}} & (13)\end{matrix}$The weight for each data point may count how many times the data pointhas been selected as an inlier by all T models. Notice that accumulatedinlier sets are not union of inlier sets, since repeated inlier datapoints are counted multiple times. To this end, the term ensemble inliersets (EIS) may be used to describe the accumulated inlier sets.

Given a scale threshold ε, the set of associate models for data point xmay be defined as a collection of permissible models that accept x as aninlier, e.g.,A _(ε)(x)={θεΘ∥ƒ(x|θ)|≦ε}.  (14)For all inliers x_(k) in set I_(ε)(θ*), corresponding associate modelsintersect and the intersection may contain θ*:

$\begin{matrix}{\theta^{*} \in {\bigcap\limits_{x_{k} \in {I_{ɛ}{(\theta^{*})}}}{{A_{ɛ}\left( x_{k} \right)}.}}} & (15)\end{matrix}$

If θ* is an optimal model (e.g., a model to be selected for use) and anappropriate ε is given, associate models for inliers A_(ε)(x_(k)) mayinclude many suboptimal models in the vicinity of θ*. In contrast,associate models of outliers may include fewer permissible models. Assuch, the relative number of associate models (e.g., the count of howmany times data points in question are selected as inliers by allpermissible models) may be used to identify inliers of the optimalmodel. Classification in this manner may be relatively insensitive todifferent scales. While it may be practically impossible to enumerateall associate models for high dimensional problems, EIS W may be usedinstead, as an estimate of the number of associate models. As such, forexample, the once scale has been determined by the scale estimator 80for various models, the model evaluator 82 may be configured to evaluateand score the models to determine a model for use in fitting.

Throughout random sampling iterations, each sampling model θ_(i),together with W, may give rise to an estimation of scale {circumflexover (ε)}_(i) according to equation (11). Since the likelihood functionmay be defined as the inverse of {circumflex over (ε)}, the maximumlikelihood scale may be taken as the minima of all estimated scales:{circumflex over (ε)}=min({circumflex over (ε)}_(i)),  (16)

The estimated {circumflex over (ε)} may then be used to update Waccording to equations (12) and (13) in the next iteration. The wholeestimation process may start from an initial ε₀ (e.g. =∞ or {circumflexover (ε)}_(MAD)) and iterates between updating W and refining{circumflex over (ε)} separately. Due to equation (16), {circumflex over(ε)} decreases monotonically. In some embodiments, under two boundaryconditions, e.g., ε→∞ and ε=0, the number of associate models may beconstant for any data points, and W may converge to a uniform weightingafter many iterations. Therefore, these two boundary conditions ensurethat {circumflex over (ε)} converges to some positive fixed point ε*ε(0,+∞).

Examples of three algorithms described herein are provided below.

Algorithm 1 RANSAC-MAD 1. Initialize ε₀ = ∞. 2. Randomly draw s datapoints and compute the model θ_(i) defined by these points. 3. Evaluatethe model and estimate {circumflex over (ε)}_(i) according to (8). 4. If{dot over (ε)}_(i) < {circumflex over (ε)}, set {circumflex over (θ)} =θ_(i) and {dot over (ε)} = {circumflex over (ε)}_(i). 5. Repeat 2-4until #MaxIter has been reached.

Algorithm 2 RANSAC-EIS 1. Initialize ε₀ = ∞, w_(n) = 1 in W = [w₁w₂ . .. w_(n)] for all points x_(n). 2. Randomly draw s data points andcompute the model θ_(i). 3. Evaluate the model and update W according to(12) and (13). 4. Estimate {circumflex over (ε)}_(i) according to (11)by using weights W. 5. If {dot over (ε)}_(i) < {circumflex over (ε)},set {circumflex over (θ)} = θ_(i) and {dot over (ε)} = {circumflex over(ε)}_(i). 6. Repeat 2-5 until #MaxIter has been reached.

Algorithm 3 RANSAC-EIS-Metropolis 1. Initialize ε₀ = ∞, assign w_(n) = 1in W = [w₁w₂ . . . w_(n)] and w_(n)′ = 1 in W_(samp) = [w₁′w₂′ . . .w_(n)′] for all point x_(n). 2. Randomly draw s data points withprobability proportional to w_(n)′, and compute the model θ_(i). 3.Evaluate the model and update W according to (12) and (13). 4. Estimate{circumflex over (ε)}_(i) according to (11) by using weights W. 5. If{circumflex over (ε)}_(i) < {dot over (ε)}, set {circumflex over (θ)} =θ_(i) and {dot over (ε)} = {circumflex over (ε)}_(i). 6. If t = 1, setθ_(s) ₁ = θ_(i) and update W_(samp). Otherwise, calculate the ratiousing (8): (17)$\alpha = {\frac{L_{MAD}\left( \theta_{i} \right)}{L_{MAD}\left( \theta_{s_{t - 1}} \right)}.}$7. Draw uniformly distributed random number U ε [0 1]. Set θ_(s) _(t) =θ_(i) and update W_(samp) if U ≦ min (α, 1), otherwise set θ_(s) _(t) =θ_(s) _(t−1) and keep W_(samp) unchanged. 8. Repeat 2-7 until #MaxIterhas been reached.

In standard RANSAC sampling, proposed models are uniformly distributedover all permissible models:

$\begin{matrix}{{{q\left( \theta_{i} \right)} = \frac{1}{C}};{\theta_{i} \in \Theta}} & (18)\end{matrix}$in which C(≈N^(s)) is the total number of all permissible models. Apotential drawback may arise in relation to equation (18) in that evenif a suboptimal model has been proposed and deemed as a good model, theprobability of hitting the nearby optimal model is still unchanged. Ahill climbing algorithm may be used to explore the neighborhood of thebest model. For example, ensemble inlier sets W may be used to achieveefficient sampling.

If s data points are randomly drawn with probability proportional tocorresponding weights ω_(n), the probability of sampling a new model θmay be given by

$\begin{matrix}{{q(\theta)} \propto {\prod\limits_{\{{n|{x_{n} \in {I_{0}{(\theta)}}}}\}}\; w_{n}}} & (19)\end{matrix}$in which I₀(θ) is a perfect inlier set of θ.

From equations (12) and (13), it may be determined that W has highweights for potentially true inlier points and low weights for outliers.Therefore, this non-uniform sampling distribution revisits highlikelihood models more often, while it pays less attention to thosemodels with low likelihood scores.

However, remember that W includes accumulated inlier sets of allproposed models. If some models are favored by the current W, they willbe more likely selected and accumulated again in the updated W. This maylead to a biased histogram with one or a few models peaked while othermodels are suppressed. In some embodiments, (e.g., see algorithm 3above), a Metropolis step may be incorporated to provide for reaching aglobally optimal model in a finite number of iterations.

In an exemplary embodiment, the score function L(·|D) in (17) may be isset as the inverse of {circumflex over (ε)}_(MAD) in equation (8)instead of {circumflex over (ε)}_(WMAD) in equation (11). ThisMetropolis step may provide that the distribution of models that areused to update W_(samp) is independent of W_(samp). With this adaptivesampling step, sampling efficiency may be improved, while theaccumulated histogram faithfully respects the input dataset.

In an exemplary embodiment, for line fitting, multiple (e.g., 2) pointsmay be randomly drawn from a dataset, and recovered models may beevaluated during each iteration (e.g., by the model evaluator 82). Foran exemplary ellipse fitting, multiple (e.g., 5) points may be drawn andan algorithm may be used to recover model parameters (e.g., by the modelevaluator 82). Ground truth line segments and ellipses may be randomlygenerated on a 2D region with x,y coordinates between a set range ofvalues. Each model may include a specified number of points and have arandom size between a set range of values. Gaussian noise with standarddeviation of a particular value may be added to the x,y coordinates ofeach inlier point.

Accordingly, based on the above descriptions, embodiments of the presentinvention may be utilized for iteratively testing different models andcorresponding scales for each of the models, in which the models beingemployed for modeling parameters correspond to visually detected data.The models may then be evaluated over several iterations in order toenable selection of a model (e.g., a best model) for use in fitting datahaving various dimensional characteristics. In the context ofembodiments of the present invention, the term visually detected datashould be understood to include both two dimensional data and also highdimensional manifold. As such, embodiments of the present invention maybe used for both identifying two dimensional objects (e.g., lines,ellipses, etc.) and/or performing transformations between two sets ofpoints. Thus, embodiments of the present invention may be employed toperform high dimensional fundamental matrix estimation for 3Dreconstruction. For fundamental matrix estimation, multiple (e.g., two)frames with a wide baseline from a corridor sequence may be used inconnection with algorithms employed for the performance of embodimentsof the present invention (e.g., algorithms 1 to 3). The ground truth forsuch sequence may be known and there may be inlier matches determinedbetween frames. Points may be randomly drawn from a dataset, and analgorithm may be used to estimate a fundamental matrix for eachiteration. As such, fundamental matrix estimation may be performed byembodiments of the present invention for various applications including,for example, an application of 3D point cloud reconstruction from acollection of photos.

FIG. 5 shows an example of fundamental matrix estimation in accordancewith an exemplary embodiment of the present invention. In this regard,FIG. 5, which includes FIGS. 5A through 5D, shows a corridor sequence inwhich there are 104 inlier matches between frames. Eight points wererandomly drawn from a dataset and a standard eight point algorithm isused to estimate F for each iteration. Gaussian noise with a standarddeviation of 1.0 is added to the 2D coordinates of inlier points. 150uniformly distributed outlier points are added to each frame. Allalgorithms repeat 10 times with 5 different threshold values.Embodiments employing EIS showed closer to a 1:1 ratio in inliers to thenumber of true inliers. FIGS. 5A and 5B show 104 true inliers (stars)and 150 outliers (dots) uniformly distributed over images. FIGS. 5C and5D show a RANSAC-EIS-Metropolis fitting result with 100 inliers, inwhich 94 are true inliers and 6 mismatch. 144 outliers and 10 trueinliers are rejected.

Embodiments of the present invention may address at least two importantaspects of RANSAC type of methods. In this regard, automatic scaleestimation may be achieved by using accumulated inlier points fromprevious RANSAC iterations. Compared with other scale estimationmethods, which often rely on mean-shift algorithms, embodiments of thepresent invention may provide a self-contained solution and may notrequire the provision of additional parameters. Furthermore, thecombination of Ensemble Inlier Sets and Weighted Median AbsoluteDeviation may provide a robust scale estimation approach withoutrequiring substantial modification from standard RANSAC algorithmapproaches. Additionally, RANSAC sampling efficiency can besignificantly boosted by using EIS-based sampling. Since no auxiliaryinformation beyond the given data is required, embodiments of thepresent invention may be readily applied to different fitting problemsas demonstrated herein. Moreover, Ensemble Inlier Sets may provide arobust and efficient computational tool suitable for any methods withrandom sampling nature.

FIG. 6 is a flowchart of a system, method and program product accordingto exemplary embodiments of the invention. It will be understood thateach block or step of the flowchart, and combinations of blocks in theflowchart, can be implemented by various means, such as hardware,firmware, and/or software including one or more computer programinstructions. For example, one or more of the procedures described abovemay be embodied by computer program instructions. In this regard, thecomputer program instructions which embody the procedures describedabove may be stored by a memory device and executed by a processor(e.g., the processor 70). As will be appreciated, any such computerprogram instructions may be loaded onto a computer or other programmableapparatus (i.e., hardware) to produce a machine, such that theinstructions which execute on the computer or other programmableapparatus create means for implementing the functions specified in theflowchart block(s) or step(s). These computer program instructions mayalso be stored in a computer-readable memory that can direct a computeror other programmable apparatus to function in a particular manner, suchthat the instructions stored in the computer-readable memory produce anarticle of manufacture including instruction means which implement thefunction specified in the flowchart block(s) or step(s). The computerprogram instructions may also be loaded onto a computer or otherprogrammable apparatus to cause a series of operational steps to beperformed on the computer or other programmable apparatus to produce acomputer-implemented process such that the instructions which execute onthe computer or other programmable apparatus provide steps forimplementing the functions specified in the flowchart block(s) orstep(s).

Accordingly, blocks or steps of the flowchart support combinations ofmeans for performing the specified functions, combinations of steps forperforming the specified functions and program instruction means forperforming the specified functions. It will also be understood that oneor more blocks or steps of the flowchart, and combinations of blocks orsteps in the flowchart, can be implemented by special purposehardware-based computer systems which perform the specified functions orsteps, or combinations of special purpose hardware and computerinstructions.

In this regard, one embodiment of a method for providing patternrecognition as provided in FIG. 6 may include iteratively testingdifferent models and corresponding scales for each of the models atoperation 100. The models may be employed for modeling parameterscorresponding to a visually detected data. The method may furtherinclude evaluating each of the models over a plurality of iterationsbased on a function evaluation of each of the models at operation 120,selecting one of the models based on the function evaluation of theselected one of the models at operation 130, and utilizing the selectedone of the models for fitting the data at operation 140.

In some embodiments, the method may include further optional operations,an example of which is shown in dashed lines in FIG. 6. In this regard,the method may further include estimating the scales of inlier datapoints for each of the models at operation 110. In an exemplaryembodiment, operation 110 may include deriving the scales based onrepeated inlier data points accumulated from the different models.

In certain embodiments, certain ones of the operations above may bemodified or further amplified as described below. It should beappreciated that each of the modifications or amplifications below maybe included with the operations above either alone or in combinationwith any others among the features described hereafter. In this regard,for example, utilizing the selected one of the models may includeutilizing the selected one of the models without any user input beyondprovision of the data. Evaluating each of the models may includeassigning a weighting factor to each respective model on the basis ofhow well each respective model fits the data and assigning a score tothe model based on the weighting factor. Assigning the weighting factormay include summing values assigned to each data point for each of themodels, the assigned values being indicative of an inlier status of eachpoint for each respective model. In some cases, selecting one of themodels may include selecting a model based on the score of the modelwithout any provision of auxiliary information by a user. In anexemplary embodiment, iteratively testing different models andcorresponding scales may include simultaneously estimating a modelparameter and a scale defining inlier data without auxiliary informationbeyond the data.

In an exemplary embodiment, an apparatus for performing the method abovemay include a processor (e.g., the processor 70) configured to performeach of the operations (100-140) described above. In some cases, theprocessor may, for example, be configured to perform the operations byexecuting stored instructions or an algorithm for performing each of theoperations. Alternatively, the apparatus may include means forperforming each of the operations described above. In this regard,according to an exemplary embodiment, examples of means for performingoperations 100 to 110 may include, for example, the scale estimator 80and/or the processor 70 and examples of means for performing operations120-140 may include, for example, the model evaluator 82 and/or theprocessor 70.

Many modifications and other embodiments of the inventions set forthherein will come to mind to one skilled in the art to which theseinventions pertain having the benefit of the teachings presented in theforegoing descriptions and the associated drawings. Therefore, it is tobe understood that the inventions are not to be limited to the specificembodiments disclosed and that modifications and other embodiments areintended to be included within the scope of the appended claims.Moreover, although the foregoing descriptions and the associateddrawings describe exemplary embodiments in the context of certainexemplary combinations of elements and/or functions, it should beappreciated that different combinations of elements and/or functions maybe provided by alternative embodiments without departing from the scopeof the appended claims. In this regard, for example, differentcombinations of elements and/or functions than those explicitlydescribed above are also contemplated as may be set forth in some of theappended claims. Although specific terms are employed herein, they areused in a generic and descriptive sense only and not for purposes oflimitation.

The invention claimed is:
 1. A method comprising: iteratively testing,at a processor, different models and corresponding scales for each ofthe models, the models being employed for modeling parameterscorresponding to a visually detected data, captured by an imagecapturing module; evaluating, by a module evaluator, each of the modelsover a plurality of iterations based on a function evaluation of each ofthe models; estimating, by a scale estimator, the scales of inlier datapoints for each of the models, wherein estimating the scales comprisesderiving the scales based on repeated inlier data points accumulatedfrom the different models; selecting, at the processor, one of themodels based on the function evaluation of the selected one of themodels; and utilizing, at the processor, the selected one of the modelsfor fitting the data; and wherein assigning a weighting factor comprisessumming values assigned to each data point for each of the models, theassigned values being indicative of an inlier status of each point foreach respective model.
 2. The method of claim 1, wherein utilizing theselected one of the models comprises utilizing the selected one of themodels without any user input beyond provision of the data.
 3. Themethod of claim 1, wherein evaluating each of the models comprisesassigning a weighting factor to each respective model on the basis ofhow well each respective model fits the data and assigning a score tothe model based on the weighting factor.
 4. The method of claim 1,wherein selecting one of the models comprises selecting a model based onthe score of the model without any provision of auxiliary information bya user.
 5. The method of claim 1, wherein iteratively testing differentmodels and corresponding scales comprises concurrently estimating amodel parameter and a scale defining inlier data without auxiliaryinformation beyond the data.
 6. A computer program product comprising atleast one non-transitory computer-readable storage medium havingcomputer-executable program code portions stored therein, thecomputer-executable program code instructions comprising: first programcode instructions for iteratively testing different models andcorresponding scales for each of the models, the models being employedfor modeling parameters corresponding to a visually detected data;second program code instructions for evaluating each of the models overa plurality of iterations based on a function evaluation of each of themodels; third program code instructions for selecting one of the modelsbased on the function evaluation of the selected one of the models;fourth program code instructions for utilizing the selected one of themodels for fitting the data; and fifth program code instructions forestimating the scales of inlier data points for each of the models,wherein the fifth program code instructions include instructions forderiving the scales based on repeated inlier data points accumulatedfrom the different models; and wherein the fourth program codeinstructions include instructions for summing values assigned to eachdata point for each of the models, the assigned values being indicativeof an inlier status of each point for each respective model.
 7. Thecomputer program product of claim 6, wherein the fifth program codeinstructions include instructions for deriving the scales based onrepeated inlier data points accumulated from the different models. 8.The computer program product of claim 6, wherein the fourth program codeinstructions include instructions for utilizing the selected one of themodels without any user input beyond provision of the data.
 9. Thecomputer program product of claim 6, wherein evaluating each of themodels comprises assigning a weighting factor to each respective modelon the basis of how well each respective model fits the data andassigning a score to the model based on the weighting factor.
 10. Thecomputer program product of claim 6, wherein the third program codeinstructions include instructions for selecting a model based on thescore of the model without any provision of auxiliary information by auser.
 11. The computer program product of claim 6, wherein the firstprogram code instructions include instructions for simultaneouslyestimating a model parameter and a scale defining inlier data withoutauxiliary information beyond the data.
 12. An apparatus comprising: amodel evaluator configured to evaluate models based on various criteria;and a processor configured to: iteratively test different models andcorresponding scales for each of the models, the models being employedfor modeling parameters corresponding to a visually detected data;control the model evaluator to evaluate each of the models over aplurality of iterations based on a function evaluation of each of themodels; select one of the models based on the function evaluation of theselected one of the models; and utilize the selected one of the modelsfor fitting the data, said apparatus further comprising a scaleestimator, wherein the processor is further configured to control thescale estimator to estimate the scales of inlier data points for each ofthe models, wherein the processor is further configured to control thescale estimator to estimate the scales by deriving the scales based onrepeated inlier data points accumulated from the different models; andassign a weighting factor by summing values assigned to each data pointfor each of the models, the assigned values being indicative of aninlier status of each point for each respective model.
 13. The apparatusof claim 12, wherein the processor is further configured to utilize theselected one of the models by utilizing the selected one of the modelswithout any user input beyond provision of the data.
 14. The apparatusof claim 12, wherein evaluating each of the models comprises assigning aweighting factor to each respective model on the basis of how well eachrespective model fits the data and assigning a score to the model basedon the weighting factor.
 15. The apparatus of claim 12, wherein theprocessor is further configured to select one of the models by selectinga model based on the score of the model without any provision ofauxiliary information by a user.
 16. The apparatus of claim 12, whereinthe processor is further configured to iteratively test different modelsand corresponding scales by simultaneously estimating a model parameterand a scale defining inlier data without auxiliary information beyondthe data.
 17. An apparatus comprising: a processor; and a memory coupledto the processor, the memory comprising computer-executable program codeportions stored therein, the computer-executable program codeinstructions, when executed by the processor, causing the apparatus to:iteratively test different models and corresponding scales for each ofthe models, the models being employed for modeling parameterscorresponding to a visually detected data; evaluate each of the modelsover a plurality of iterations based on a function evaluation of each ofthe models; select one of the models based on the function evaluation ofthe selected one of the models; and utilize the selected one of themodels for fitting the data, wherein the computer-executable programcode instructions further cause the apparatus to estimate the scales ofinlier data points for each of the models, and to estimate the scales byderiving the scales based on repeated inlier data points accumulatedfrom the different models; and assign a weighting factor by summingvalues assigned to each data point for each of the models, the assignedvalues being indicative of an inlier status of each point for eachrespective model.